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  <div class="section" id="gran-rolling-friction-epsd-model">
<span id="index-0"></span><h1>gran rolling_friction epsd model<a class="headerlink" href="#gran-rolling-friction-epsd-model" title="Permalink to this headline">¶</a></h1>
<div class="section" id="syntax">
<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
<pre class="literal-block">
rolling_friction epsd [other model_type/model_name pairs as described <a class="reference internal" href="pair_gran.html"><em>here</em></a> ] keyword values
</pre>
<ul class="simple">
<li>zero or more keyword/value pairs may be appended to the end (after all models are specified)</li>
</ul>
<pre class="literal-block">
<em>torsionTorque</em> values = 'on' or 'off'
  on = also the normal, relative rotation (torsion) contributes to the resulting torque
  off = only the tangential, relative rotation contributes to the resulting torque
</pre>
</div>
<div class="section" id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
<p>This model can be used as part of <a class="reference internal" href="pair_gran.html"><em>pair gran</em></a> and
<a class="reference internal" href="fix_wall_gran.html"><em>fix wall/gran</em></a></p>
<p>The elastic-plastic spring-dashpot (EPSD) model (see Ai et al.) adds an additional
torque contribution, equal to</p>
<img alt="_images/pair_gran_hooke_eqEpsd1.gif" class="align-center" src="_images/pair_gran_hooke_eqEpsd1.gif" />
<p>where the torque due to the spring M_rk is calculated as</p>
<img alt="_images/pair_gran_hooke_eqEpsd2.gif" class="align-center" src="_images/pair_gran_hooke_eqEpsd2.gif" />
<p>Here k_r denotes the rolling stiffness that depends on the stiffness of the normal spring (from the normal contact law), the effective radius and the coefficient of rolling friction (mu_r). Following <strong>(Ai)</strong> the prefactor of 2.25 is valid for 3D simulations. The <a class="reference internal" href="gran_rolling_friction_epsd3.html"><em>EPSD3 model</em></a> allows to modify the prefactor. dtheta_r is the incremental relative
rotation between the particles. The spring torque is limited by the full mobilisation
torque M_rm that is determined by the normal force F_n and the coefficient of rolling
friction (mu_r) (compare the <a class="reference internal" href="gran_rolling_friction_cdt.html"><em>CDT model</em></a>).</p>
<p>The viscous damping torque M_rd is implemented as</p>
<img alt="_images/pair_gran_hooke_eqEpsd3.gif" class="align-center" src="_images/pair_gran_hooke_eqEpsd3.gif" />
<p>where in the current implementation the damping is disabled in case of full mobilisation
(f = 0). The damping coefficient C_r may be expressed as:</p>
<img alt="_images/pair_gran_hooke_eqEpsd4.gif" class="align-center" src="_images/pair_gran_hooke_eqEpsd4.gif" />
<p>Here I_i/j is the moment of inertia and m_i/j is the mass of the particles i and j,
respectively.</p>
<p>The coefficient of rolling friction (mu_r) must be defined as</p>
<div class="highlight-python"><div class="highlight"><pre>fix id all property/global coefficientRollingFriction peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for the coefficient of rolling friction between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation)
</pre></div>
</div>
<p>This coefficient mu_r is equal to the mu_r as defined in the <a class="reference internal" href="gran_rolling_friction_cdt.html"><em>CDT model</em></a>.
In addition to mu_r, eta_r is the required material property that must be defined as</p>
<div class="highlight-python"><div class="highlight"><pre>fix id all property/global coefficientRollingViscousDamping peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for the coefficient of rolling friction between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation)
</pre></div>
</div>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">You have to use atom styles beginning from 1, e.g. 1,2,3,...</p>
</div>
<p><strong>Torque information:</strong></p>
<p>By default the relative, normal rotation (torsion) is subtracted and does not contribute to the resulting torque. By setting the <em>torsionTorque</em> keyword to &#8216;on&#8217;, the full relative rotation contributes to the rolling friciton torque.</p>
<p><strong>Coarse-graining information:</strong></p>
<p>Using <code class="xref doc docutils literal"><span class="pre">coarsegraining</span></code> in
combination with this command might lead to
different dynamics or system state and thus to
inconsistencies.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last"><code class="xref doc docutils literal"><span class="pre">Coarsegraining</span></code> may or
may not be available in LIGGGHTS(R)-PUBLIC.</p>
</div>
</div>
<div class="section" id="default">
<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
<p><em>torsionTorque</em> = &#8216;off&#8217;</p>
<p><strong>(Ai)</strong> Jun Ai, Jian-Fei Chen, J. Michael Rotter, Jin Y. Ooi, Powder Technology, 206 (3), p 269-282 (2011).</p>
</div>
</div>


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